Is it a good idea to add a female cat?

Yes the tom will probably "dominate" the female -- but the female isn't a human being with ideals of fairness and equality and will probably cope with it just fine. 

Don't count on them ever being affectionate with each other, or even friendly. When Pluto was about 4 years old, I added Turbo to our home. Fast forward 16 years and they could still barely stand to be in the same room. But when Turbo had kidney failure and passed, poor Pluto grieved and mourned and pined as if he'd lost his best friend. 

Don't count a second cat changing your dog's behavior. Sounds to me like the dog needs more exercise, more interests and challenges in his life. Can you get him those "puzzle" dog toys where he has to work on it and work on it some more to get a single kibble of food out of it? Can you create safe havens for your cat(s) where they can nap, hang out, look out the window but the dog can't get at them? 

If you get another cat, do it because YOU want another cat. If you feel like it's a sacrifice, then don't do it; you'll just come to resent and regret. 

When you bring a new animal into the home, keep it separated from the "old" animals and out of sight. Bring the old animals, one at a time, to look at the new animal, and the whole time keep giving the old animal wee bits of treat. The idea to brainwash your old animals, to get their brains working along the lines of "I can't stand that little creep but every time I see him wonderful things happen." 

When the old animals are reconciled to SEEING the newcomer without all that stress and anger, THEN gradually -- and with plenty of supervision -- bring them into closer and closer contact. All the while keeping that old animal so occupied with tiny treats that he/she is too busy for hostile displays. 

Good luck with your "family." 

No, i think two pets are enough for any house.

Yes. Cats like company. They will have fun playing and snuggling.

I would suggest not bringing another pet into your household. One of the biggest mistakes that people make is assuming their pets "need friends," when in reality, all they want is to keep the same routine and to be left alone. Pet ownership is not like a Disney movie at all; at best, you can expect cats and dogs to merely tolerate each other and go on with their lives. Those videos you see of cats snuggling with dogs are very few and far between, and most likely due to the owners either getting them together when they were very young, or adopting animals that already had years of cat/dog experience, but again, gained when they were very young and didn't know any better. 

Play with the cat for 20 minutes a day, in a room, by yourselves, treat the cat, the end. This will increase the bond, give the cat some alone time with you, and leave the dog out of it. Your cat still needs to feel special. Your dog needs to put up with it. I'm sure you play, walk, love your dog, but the dog has to realize he's not the only one that needs love and attention. My pup LOVES to harass my cats; one hates him with a passion, the other doesn't bother engaging and the dog gives up. I don't think I will ever catch them snuggling together all cute and peaceful, at least not until the dog is older. I'm not going to make the mistake of getting another dog right now, thinking my pup needs a playmate. 

Recipe for disaster. The Male cat will dominate the female, and the dog will terrorise both.